Open AccessSeparation axioms in topological preordered spaces and the existence of continuous order-preserving functions
Author(s) -
Gianni Bosi,
Romano Isler
Publication year - 2000
Publication title -
applied general topology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.638
H-Index - 13
eISSN - 1989-4147
pISSN - 1576-9402
DOI - 10.4995/agt.2000.3026
Subject(s) - preorder , mathematics , topological space , space (punctuation) , order (exchange) , function space , separation axiom , axiom , pure mathematics , real valued function , topology (electrical circuits) , function (biology) , continuous function (set theory) , discrete mathematics , combinatorics , computer science , geometry , finance , evolutionary biology , economics , biology , operating system
We characterize the existence of a real continuous order-preserving function on a topological preordered space, under the hypotheses that the topological space is normal and the preorder satisfies a strong continuity assumption, called IC-continuity. Under the same continuity assumption concerning the preorder, we present a sufficient condition for the existence of a continuous order-preserving function in case that the topological space is completely regular